Question

Please help me I need to show my work too!

Answer 1

1. X = 28.9
2. X = 2.7
3. X = 25.7

Explanation:

To label the sides with information (opposite, adjacent, or hypotenuse) we know that the longest side of the triangle or the side that is always opposite from the 90° angle is hypotenuse. The side that is opposite from the given angle is labeled opposite. The side that is adjacent to the given angle is labeled adjacent.

Because we already have the formulas of SOHCAHTOA we can easily solve for x.

For ΔTUV we solve for x by using TOA. We use this trig function because our given side 8.3 is opposite from ∠16°and the side we are trying to find is adjacent to ∠16°. So we set up our equation like this:

`tan16=(8.3)/(x)`

For ΔFED we solve for x by using SOH. We use this trig function because our given side 1.7 is opposite from ∠39°and the side we are trying to find is the hypotenuse. So we set up our equation like this:

`sin39=(1.7)/(x)`

For ΔSTU we solve for x by using CAH. We use this trig function because our given side 27 is the hypotenuse and the side we are trying to find is adjacent to ∠18°. So we set up our equation like this:

`cos18=(x)/(27)`

Now we just solve for x